Improper fractions, mixed numbers and like fractions · Usually met around P4
Improper fractions and mixed numbers
Top ÷ bottom: whole part, remainder on top.
How to do it
Method
Top ÷ bottom: whole part, remainder on top
175 = 3 25 (5 × 3 = 15, 17 − 15 = 2)
One more example
2 34 = (2 × 4 + 3)/4 = 114
In full
If a fraction's top is the same as or bigger than its bottom, it's an improper fraction, like 175. A whole number and a proper fraction together make a mixed number, like 3 25, which means 3 + 25. Improper to mixed: divide the top by the bottom. The quotient is the whole part, and the remainder is the new top, over the same bottom. 175: how many 5s in 17? 5 × 3 = 15, 17 − 15 = 2, so 175 = 3 25. If the top is a multiple of the bottom, you get a whole number: 124 = 12 ÷ 4 = 3. Mixed to improper: multiply the whole number by the bottom, add the top, and put it over the same bottom: 2 34 → 2 × 4 = 8, 8 + 3 = 11, so 2 34 = 114. Or split the mixed number: 2 34 = 2 + 34 = 84 + 34 = 114.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
357 = ?
Show the answer and working
Answer: 357 = 5
357: the numerator is a multiple of the denominator, so it's a whole number: 35 ÷ 7 = 5
Example 2
8 19 = ?
Answer as an improper fraction
Show the answer and working
Answer: 8 19 = 739
8 19: the whole number times the denominator, plus the numerator, over the same denominator: 8 × 9 = 72, 72 + 1 = 73 → 739
Example 3
6 78 = ?
Answer as an improper fraction
Show the answer and working
Answer: 6 78 = 558
6 78: the whole number times the denominator, plus the numerator, over the same denominator: 6 × 8 = 48, 48 + 7 = 55 → 558
Practise it in the game →Improper fractions, mixed numbers and like fractions · Free to start, unlimited questions, no download